Abstract Details
Abstracts
Author: Joshua W. Burby
Requested Type: Pre-Selected Invited
Submitted: 2017-03-10 15:47:11
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Contact Info:
Courant Institute of Mathematical Sciences
251 Mercer St
New York, NY 10012
USA
Abstract Text:
Magnetohydrodynamics (MHD) is often derived from the two-fluid model of a plasma, which is known to support a rich variety of dynamical processes that are completely absent from MHD. In particular light waves and Langmuir oscillations are present in two-fluid theory, but not in MHD. What is the mechanism by which the two-fluid processes missing from MHD become dynamically irrelevant within two-fluid theory? Here I will discuss one such mechanism. Using the mathematical technique known as slow manifold reduction, I will show that there are special "slow" initial conditions for the two-fluid model that are governed essentially by (extended) MHD. These initial conditions generate two-fluid motions that do not excite the dynamical processes missing from MHD. Light waves and Langmuir waves are not ``averaged out" -- they are inactive. Because the (frictionless) two-fluid theory is a Hamiltonian system, the dynamics of the slow initial conditions inherits its own Hamiltonian structure. I will provide a closed-form expression for the corresponding functional Poisson bracket, as well as the leading-order terms in the Hamiltonian functional.
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